Superlubricity between incommensurate surfaces provides a desired low-friction state essential for the function of small-scale machines. Here we demonstrate experimentally and theoretically that superlubricity in contacts lubricated by lamellar solids might be eliminated due to torque-induced reorientation coupled to lateral motion. We find that the possibility of reorientation always leads to stabilization of a high frictional state which corresponds to a commensurate configuration.